Question

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complete the proof that ( overline{gi} cong overline{gh} ).

Explanation:

Step1: Determine the congruent triangles

Since we have \(\angle GJH\cong\angle GJI\), \(\angle H\cong\angle I\), and \(\overline{GJ}\cong\overline{GJ}\), by the AAS (Angle - Angle - Side) congruence criterion, \(\triangle GJH\cong\triangle GJI\).

Step2: Use the property of congruent triangles

If two triangles are congruent, then their corresponding sides are congruent. So, \(\overline{GI}\cong\overline{GH}\) because they are corresponding sides of congruent triangles \(\triangle GJH\) and \(\triangle GJI\).

Answer:

1. \(\triangle GJH\cong\triangle GJI\) (Reason: AAS Congruence Criterion); \(\overline{GI}\cong\overline{GH}\) (Reason: Corresponding parts of congruent triangles are congruent)